The polygon approximation method uses the perimeters of polygons to approximate pi and "was the first theoretical, rather than measured, calculation of pi", but while it worked great for Archimedes in his time, it has limited practicality today (Groleau). To estimate pi, Archimedes used a circle in which a polygon was inscribed and circumscribed, then found the perimeter of each polygon and used those values ​​as the upper and lower limits of pi (Groleau). He began with a hexagon as the interior polygon of a circle with a diameter of 1 whose perimeter is equal to 6r when r is the radius of the circle (McKeeman). This meant that since the circumference of the circle was 2πr, 6r < 2πr and the lower limit of pi was 3 (McKeeman). He then found the perimeter of the outer hexagon to calculate the upper limit and proceeded to double the number of sides and repeat the operation